The blades of turbine machines, such as the compressor and turbine blades of jet engines, are subject to erosive wear, especially at the area of the blade tips. In the past, it has then been necessary to completely replace the entirety of the worn turbine blades. However, for cost reasons, a method of repairing only the worn blade tips, instead of completely replacing the entire worn blades, is needed. Heretofore, worn blade tips have been repaired by machining down the worn tips to remove the respective worn blade portion, and then re-applying the missing material, for example, by means of microplasma deposit welding. The published article "Instandhaltung von Dampfturbinen-Endstufenschaufeln" ("Repair of Steam Turbine End Stage Blades") by W. Storch et al. in BWK, Vol. 45, No. 5 (May 1993), pages 240 to 246, and particularly page 242, describes such a known repair method. A disadvantage of such a known method is the relatively high effort required for carrying out mechanical after-machining or finish-machining, which becomes ever greater as the width of the weld bead of the applied material increases.